Time Measurement CS 201 Gerson Robboy Portland State University Topics Time scales Interval counting Cycle counters K-best measurement scheme

– 2 – Computer Time Scales Two Fundamental Time Scales Processor: ~10 –9 sec. External events: ~10 –2 sec. Keyboard input Disk seek Screen refreshImplication Can execute many instructions while waiting for external event to occur Can alternate among processes without anyone noticing Time Scale (1 Ghz Machine) 1.E-091.E-061.E-031.E+00 Time (seconds) 1 ns 1  s 1 ms1 s Integer Add FP Multiply FP Divide Keystroke Interrupt Handler Disk Access Screen Refresh Keystroke Microscopic Macroscopic

– 3 – Measurement Challenge How Much Time Does Program X Require? CPU time How many total seconds are used when executing X? Small dependence on other system activities Actual (“Wall”) Time How many seconds elapse between the start and the completion of X? Depends on system load, I/O times, etc. Confounding Factors How does time get measured? Many processes share computing resources

– 4 – “Time” on a Computer System real (wall clock) time = user time (time executing instructions in the user process) += real (wall clock) time We will use the word “time” to refer to user time. = system time (time executing instructions in kernel on behalf of user process) + = some other user’s time (time executing instructions in different user’s process) cumulative user time

– 5 – Activity Periods: Light Load Most of the time spent executing one process Periodic interrupts every 10ms Interval timer Schedules processes to run Other interrupts Due to I/O activity Inactivity periods System time spent processing interrupts ~250,000 clock cycles Activity Periods, Load = Time (ms) Active Inactive

– 6 – Activity Periods: Heavy Load Sharing processor with one other active process From perspective of this process, system appears to be “inactive” for ~50% of the time Other process is executing Activity Periods, Load = Time (ms) Active Inactive

– 7 – Interval Counting OS Measures Runtimes Using Interval Timer In other words, statistical sampling. Similar to profiling. Maintain 2 counts per process User time System time On each timer interrupt, increment counter for executing process User time if running in user mode System time if running in kernel mode

– 8 – Interval Counting Example Au AsBuBsBu AsAu BsBu BsAu As (a) Interval Timings BBAAA (b) Actual Times B AA B A120.0u s B73.3u s A Au AsBuBsBu AsAu BsBu BsAu As (a) Interval Timings BBAAA Au AsBuBsBu AsAu BsBu BsAu As (a) Interval Timings BBAAA (b) Actual Times B AA B A120.0u s B73.3u s A (b) Actual Times B AA B A120.0u s B73.3u s A Exercise: What timings does the interval timer give us for Au, As, Bu, and Bs? How far off are they from “actual?”

– 9 – Unix time Command 0.82 seconds user time 82 timer intervals 0.30 seconds system time 30 timer intervals 1.32 seconds wall time 84.8% of total was used running these processes ( )/1.32 =.848 Exactly what process or processes are using that.82 of user time? time make osevent gcc -O2 -Wall -g -march=i486 -c clock.c gcc -O2 -Wall -g -march=i486 -c options.c gcc -O2 -Wall -g -march=i486 -c load.c gcc -O2 -Wall -g -march=i486 -o osevent osevent.c u 0.300s 0: % 0+0k 0+0io 4049pf+0w

– 10 – Accuracy of Interval Counting Worst Case Analysis Single process segment measurement can be off by how much? No bound on error for multiple segments Could consistently underestimate, or consistently overestimate Pretty unlikely A A Minimum Maximum A A Minimum Maximum Computed time = 70ms Min Actual = 60 +  Max Actual = 80 – 

– 11 – Accuracy of Int. Cntg. (cont.) Average Case Analysis Over/underestimates tend to balance out As long as total run time is sufficiently large Min run time ~1 second 100 timer intervals Consistently miss 4% overhead due to timer interrupts A A Minimum Maximum A A Minimum Maximum Computed time = 70ms Min Actual = 60 +  Max Actual = 80 – 

– 12 – Cycle Counters Most modern systems have built in registers that are incremented every clock cycle Very fine grained Elapsed global time (“wall clock” time) Accessed with a special instruction On (recent model) Intel machines: It’s a 64 bit counter called the time stamp counter. Accessed with RDTSC instruction RDTSC sets %edx to high order 32-bits, %eax to low order 32-bits

– 13 – Cycle Counter Period Wrap Around Times for 550 MHz machine Low order 32 bits wrap around every 2 32 / (550 * 10 6 ) = 7.8 seconds High order 64 bits wrap around every 2 64 / (550 * 10 6 ) = seconds 1065 years For 2 GHz machine Low order 32-bits every 2.1 seconds High order 64 bits every 293 years

– 14 – Measuring with Cycle Counter Main Idea Get current value of cycle counter store as pair of unsigned’s cyc_hi and cyc_lo Compute something Get new value of cycle counter Perform double precision subtraction to get elapsed cycles /* Keep track of most recent reading of cycle counter */ static unsigned cyc_hi = 0; static unsigned cyc_lo = 0; void start_counter() { /* Get current value of cycle counter */ access_counter(&cyc_hi, &cyc_lo); }

– 15 – So how do you implement access_counter() in C? Need to do an RDTSC instruction. One way: Write a function in assembly language, in a separate source file, conforming to the C language call/return conventions. An easier way with gcc: Use inline assembly code When you see the syntax, you may not believe it’s easier

– 16 – Accessing Linux Cycle Counter GCC allows inline assembly code with mechanism for matching registers with program variables This only works on x86 machine compiling with GCC Emit assembly with rdtsc and two movl instructions void access_counter(unsigned *hi, unsigned *lo) { /* Get cycle counter */ asm("rdtsc; movl %edx,%0; movl %eax,%1" : "=r" (*hi), "=r" (*lo) : /* No input */ : "%edx", "%eax"); }

– 17 – Extended ASM: A Closer Look Instruction String Series of assembly commands Separated by “;” or “\n” Use “%” where normally would use “%” asm(“Instruction String" : Output List : Input List : Clobbers List); } void access_counter (unsigned *hi, unsigned *lo) { /* Get cycle counter */ asm("rdtsc; movl %edx,%0; movl %eax,%1" : "=r" (*hi), "=r" (*lo) : /* No input */ : "%edx", "%eax"); }

– 18 – Extended ASM, Cont. Output List Expressions indicating destinations for values %0, %1, …, %j Enclosed in parentheses Must be lvalue »Value that can appear on LHS of assignment Tag "=r" indicates that symbolic value (%0, etc.), should be replaced by register asm(“Instruction String" : Output List : Input List : Clobbers List); } void access_counter (unsigned *hi, unsigned *lo) { /* Get cycle counter */ asm("rdtsc; movl %edx,%0; movl %eax,%1" : "=r" (*hi), "=r" (*lo) : /* No input */ : "%edx", "%eax"); }

– 19 – Extended ASM, Cont. Input List Series of expressions indicating sources for values %j+1, %j+2, … Enclosed in parentheses Any expression returning value Tag "r" indicates that symbolic value (%0, etc.) will come from register asm(“Instruction String" : Output List : Input List : Clobbers List); } void access_counter (unsigned *hi, unsigned *lo) { /* Get cycle counter */ asm("rdtsc; movl %edx,%0; movl %eax,%1" : "=r" (*hi), "=r" (*lo) : /* No input */ : "%edx", "%eax"); }

– 20 – Extended ASM, Cont. Clobbers List List of register names that get altered by assembly instruction Compiler will make sure doesn’t store something in one of these registers that must be preserved across asm Value set before & used after asm(“Instruction String" : Output List : Input List : Clobbers List); } void access_counter (unsigned *hi, unsigned *lo) { /* Get cycle counter */ asm("rdtsc; movl %edx,%0; movl %eax,%1" : "=r" (*hi), "=r" (*lo) : /* No input */ : "%edx", "%eax”); }

– 21 – Accessing Cycle Counter, Cont. Emitted Assembly Code Used %ecx for *hi (replacing %0) Used %ebx for *lo (replacing %1) Does not use %eax or %edx for value that must be carried across inserted assembly code movl 8(%ebp),%esi# hi movl 12(%ebp),%edi# lo rdtsc; movl %edx,%ecx; movl %eax,%ebx movl %ecx,(%esi)# Store high bits at *hi movl %ebx,(%edi)# Store low bits at *lo

– 22 – Accessing the Cycle Cntr. (cont.) Now are you convinced you’ll never write one of those? Relax, no one ever does, from scratch. Start with an existing snippet of code that looks pretty much like what you want. Inline assembly really comes in handy sometimes, once you get used to it.

– 23 – Completing the Measurement Perform double precision subtraction to get elapsed cycles Express as double to avoid overflow problems double get_counter() { unsigned ncyc_hi, ncyc_lo unsigned hi, lo, borrow; /* Get cycle counter */ access_counter(&ncyc_hi, &ncyc_lo); /* Do double precision subtraction */ lo = ncyc_lo - cyc_lo; borrow = lo > ncyc_lo; hi = ncyc_hi - cyc_hi - borrow; return (double) hi * (1 << 30) * 4 + lo; } Why do they do this? borrow = lo > ncyc_lo;

– 24 – Timing With Cycle Counter Determine Clock Rate of Processor Count number of cycles required for some fixed number of seconds Time Function P First attempt: Simply count cycles for one execution of P double tsecs; start_counter(); P(); tsecs = get_counter() / (MHZ * 1e6); double MHZ; int sleep_time = 10; start_counter(); sleep(sleep_time); MHZ = get_counter()/(sleep_time * 1e6);

– 25 – Measurement Pitfalls Overhead Calling get_counter() incurs small amount of overhead Want to measure long enough code sequence to compensate Unexpected Cache Effects artificial hits or misses e.g., these measurements were taken with the Alpha cycle counter: foo1(array1, array2, array3); /* 68,829 cycles */ foo2(array1, array2, array3); /* 23,337 cycles */ vs. foo2(array1, array2, array3); /* 70,513 cycles */ foo1(array1, array2, array3); /* 23,203 cycles */

– 26 – Dealing with Cache Effects Execute function once to “warm up” the cache Both data and instructions P();/* Warm up cache */ start_counter(); P(); cmeas = get_counter(); Issue: Some functions don’t execute in cache Depends on both the algorithm and the data set Need to do measurements with appropriate data

– 27 – Multitasking Effects Cycle Counter Measures Elapsed Time Keeps accumulating during periods of inactivity System activity Running other processes Key Observation Cycle counter never underestimates program run time Possibly overestimates by large amount K-Best Measurement Scheme Perform up to N (e.g., 20) measurements of function See if fastest K (e.g., 3) within some relative factor  (e.g., 0.001) K

– 28 – K-Best Validation Very good accuracy for < 8ms Within one timer interval Even when heavily loaded Less accurate of > 10ms Light load: ~4% error Interval clock interrupt handling Heavy load: Very high error K = 3,  = 0.001

– 29 – Time of Day Clock Unix gettimeofday() function Return elapsed time since reference time (Jan 1, 1970) Implementation Uses interval counting on some machines »Coarse grained Uses cycle counter on others »Fine grained, but significant overhead and only 1 microsecond resolution #include struct timeval tstart, tfinish; double tsecs; gettimeofday(&tstart, NULL); P(); gettimeofday(&tfinish, NULL); tsecs = (tfinish.tv_sec - tstart.tv_sec) + 1e6 * (tfinish.tv_usec - tstart.tv_usec);

– 30 – Nice things about gettimeofday() Portable! Portable! No need to do double-precision integer arithmetic No need to do double-precision integer arithmetic 1 Microsecond resolution is pretty good for most purposes 1 Microsecond resolution is pretty good for most purposes

– 31 – K-Best Using gettimeofday Linux As good as using cycle counter For times > 10 microsecondsWindows Implemented by interval counting Too coarse-grained

– 32 – Measurement Summary Timing is highly case and system dependent What is overall duration being measured? > 1 second: interval counting is OK << 1 second: must use cycle counters On what hardware / OS / OS version? Accessing counters »How gettimeofday is implemented Timer interrupt overhead Scheduling policy Devising a Measurement Method Long durations: use Unix timing functions Short durations If possible, use gettimeofday Otherwise must work with cycle counters K-best scheme most successful